Second order cone programming relaxation of a positive semidefinite constraint

Sunyoung Kim; Masakazu Kojima; Makoto Yamashita

doi:10.1080/1055678031000148696

Second order cone programming relaxation of a positive semidefinite constraint

Sunyoung Kim, Masakazu Kojima, Makoto Yamashita

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of expressing the positive semidefinite constraint of the SDP relaxation. We present how such SOCP relaxations can be derived, and show the relationship between the resulting SOCP relaxations.

Original language	English
Pages (from-to)	535-541
Number of pages	7
Journal	Optimization Methods and Software
Volume	18
Issue number	5
DOIs	https://doi.org/10.1080/1055678031000148696
State	Published - Oct 2003

Keywords

Convex relaxation
Nonconvex program
Quadratic program
Second order cone program
Semidefinite program

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10.1080/1055678031000148696

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abstract = "The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of expressing the positive semidefinite constraint of the SDP relaxation. We present how such SOCP relaxations can be derived, and show the relationship between the resulting SOCP relaxations.",

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AB - The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of expressing the positive semidefinite constraint of the SDP relaxation. We present how such SOCP relaxations can be derived, and show the relationship between the resulting SOCP relaxations.

KW - Convex relaxation

KW - Nonconvex program

KW - Quadratic program

KW - Second order cone program

KW - Semidefinite program

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Second order cone programming relaxation of a positive semidefinite constraint

Abstract

Keywords

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